bear - ingn.1 the manner in which one comports oneself; 2 the act, power, or time of bringing forth offspring or fruit; 3 a machine part in which another part turns [a journal ~]; 4pl. comprehension of one's position, environment, or situation; 5 the act of moving while supporting the weight of something [the ~ of the cross].

14 July 2007

String theory: an optimization problem.

This morning I placed a polyethylene bag full of fresh string beans on the kitchen counter in front of me. I set a metal colander at my right hand. I tore open the bag of beans. With my left hand I picked up one bean and examined it briefly, turning it in my two hands until my left (dominant) hand grasped the stem end. I pinched the bean just below the stem, between my index fingernail and the pad of my thumb; my left hand then held an amputated green-bean stem and my right hand held the long end of the bean. I dropped the stem onto the counter and grasped the bean again, holding both ends, then broke it in half. I passed the half held in my left hand to my right hand and with my right hand dropped both beans into the colander. I picked up another bean. The piles of stems to the left and beans to the right grew slowly.

There were about two and a half pounds of green beans to trim. It's not a bad job; the mind can wander. Today I thought about the way I was doing it. Could I be more efficient? I tried speeding up and dropped a bean. No good. I went over each step in my mind:

pick up random bean in left hand

grasp bean with right hand

rotate bean into position

pinch stem off bean

throw stem to the left

grasp end of bean with left hand

break bean with both hands

pass bean halves to right hand

put bean halves in colander to the right

Could I go faster if I pinched the stem off with my right hand? I tried it for a couple of beans and concluded that my first unconscious choice, left-handed stem-pinching, had been the most reproducibly successful one; right-handed, I take off more stem than I usually want. (Of course, I mused as I turned a bean between my fingers, it's not appropriate to think of the stem-removal operation as "left-handed" or "right-handed." One hand steadies the bean, the other hand pinches the stem, and the person that manages the hands distributes the tasks as best as she can.)

Then I turned my attention to breaking the bean in half. I realized that if I could alter step 7 by somehow breaking each bean in half with one hand -- my right hand -- I could eliminate steps 6 and 8. After a little experimentation and practice, I was able to develop a one-handed, non-dominant-hand bean-snap.

Pleased, I went on with the beans. I did seem to be going faster. But the question dogged me... was I going optimally fast?

As I worked, I realized with irritation that I was needlessly over-handling the beans. I had learned in my earlier stem-pinching experiments that I could not eliminate step 2 without undesirable results. One-handed stem-removal was a path that I had already tried and found wanting. But why, I thought, did I have to rotate the bean between picking up the bean and pinching off the stem? I have some control over the bean-choosing, bean-picking process, don't I? Why not just pick up the bean more carefully, so that it's already in position in my left hand by the time my right hand arrives to grasp it?

I happen to have a pretty good machine vision system, at least when I remember to put on my glasses, so it was trivial to develop a new bean-choosing algorithm. It only took a little bit more attention, and less time, to watch my left hand as it dipped into the bag of beans (which I was beginning to see as an ensemble of rigid rods having a certain distribution of lengths, diameters, orientations, etc.), and to pick up each bean between index fingernail and thumb, positioned at the point where I wished to sever the stem, and with my wrist oriented in such a way that when I brought hand and wrist back to a neutral position, they would naturally rotate the bean so that at the very moment my right hand grasped it I could sever the stem.

Grabbing the beans in position took more attention than I realized, especially as the number of easy-to-grab bean stems dwindled, but I quickly saw the superiority of the new system. I had reduced the number of physical steps to six:

pick up bean carefully in position in left hand

grasp bean in right hand

pinch stem off bean

throw stem to the left

snap bean in right hand

throw bean halves into the colander

Only one of the steps, number one, had gotten significantly more complicated, and all of the complication was in processing. I have plenty of memory and my processor speed is high compared to my bean-handling speed, so this was hardly a trade-off. I suppose I don't get to let my mind wander quite as much.